Finite difference formulation of shape detection using Poisson’s equation

Object can be detected or compared its similarity to other shapes, when shape detection is successfully described in computer vision. In this study, three geometry shapes are used in shape detection which are square, circle and ellipse. The two dimensional (2D) Poisson’s equation is used to detect these shapes because Poisson’s equation can be used for various types of shape detection. In order to approximate the Poisson’s equation, the discretization process is conducted using an implicit finite difference method. The Jacobi and Gauss-Seidel methods have been used to solve linear equation of 2D Poisson’s equation. The numerical algorithms are developed in MATLAB R2012b software. In the solution process, the Gauss-Seidel method used less number of iterations compared to Jacobi method to detect square, circle and ellipse. Numerical solutions for these methods are compared and the results obtained using these methods are found to be efficient and suitable to obtain the original shape. The simulation results of 2D Poisson’s equation have been successfully predicted for the shape detection.